QC 


x^.— 


SB    bD7    157 


J 

M 


JA! 

(iljr  .lliilmu  Bunkum  Hmveratt) 


Magnetic  Rotatory  Dispersion 
in  Transparent  Liquids 


DISSERTATION 
SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES  OF  THE  JOHNS 

UNIVERSITY  IN  CONFORMITY  WITH  THE  REQUIREMENTS  FOR  THE 
DEGREE  OF  DOCTOR  OF  PHILOSOPHY 


June  1921 


ROBERT  ALLEN  CASTLEMAN,  JR. 


Baltimore,  Md. 
1921 


MAGNETIC  ROTARY  DISPERSION  IN  TRANS- 
PARENT LIQUIDS 

BY  R.  A.  CASTLEMAN,  JR.,  AND  E.  O.  HULBURT 

ABSTRACT 

Magnetic  rotary  dispersion  of  isotropic  transparent  media.  —  The  electron  theory 
as  given  by  H.  A.  Lorentz  is  extended,  and  a  formula  for  the  rotation  in  a  range  of 
spectrum  in  which  electrons  of  only  a  single  type,  with  critical  frequency  c/Xi,  need 
be  considered,  is  developed: 


2 

H  is  field  strength,  I  is  length,  /*  is  refractive  index,  c  is  velocity  of  light,  and  a  is  a 
constant  which  Lorentz  puts  equal  to  about  \  and  Voigt  puts  equal  to  zero.  To  test 
this  theory,  substances  were  chosen  whose  dispersion  was  known  to  conform  to  the 
theory  of  Lorentz,  and  the  magnetic  rotations  for  carbon  disulphide,  a-monobromnaph- 
thalene,  benzene,  nitrobenzene  and  ethyl  iodide  for  six  wave-lengths  from  436  to  620  /z/x 
were  determined  with  a  cell  2  cm  long  in  a  field  of  6480  gauss.  The  angles  could  be 
measured  to  iV  and  were  found  to  vary  from  4°  to  28°,  increasing  rapidly  for  eacb 
liquid  with  decreasing  wave-length.  •  Theoretical  curves  were  computed,  taking  the 
values  of  Ci,  Xx  and  /u  from  measurements  by  others.  Below  590  up  the  experimental 
curves  lie  below  the  theoretical  curves,  the  divergence  increasing  as  the  wave-length 
diminishes  until  the  difference  at  423  /x/x  is  from  4  to  20  per  cent.  It  is  suggested 
that  this  discrepancy  is  due  to  the  absorption  of  the  violet  end  of  the  spectrum  which 
was  neglected  in  the  theory.  The  results  do  not  decide  between  the  values  o  and  \  for 
a.  The  values  of  e/m  for  the  active  electrons  may  be  computed  from  ht  and  vary  from 
0.5  to  i  .  78  X  io7  e.m.u.  according  to  the  liquid  and  to  the  value  of  <r  assumed. 

i.  Introductory.  —  -In  1845  Faraday  discovered  that  isotropic 
substances  when  placed  in  a  strong  longitudinal  magnetic  field 
rotate  the  plane  of  polarization  of  plane-polarized  light.  The 
obvious  explanation  of  this,  confirmed  later  by  Brace,  was  the 
same  as  that  offered  by  Fresnel  for  the  rotation  observed  in  certain 
crystals,  viz.,  to  consider  the  plane-polarized  beam  to  be  com- 
posed of  two  circularly  polarized  components  which  travel  through 
the  medium  with  different  velocities,  one  greater  and  the  other 
less  than  the  velocity  of  the  beam"  in  the  medium  when  unmag- 
netized.  The  variation  of  the  angle  of  magnetic  rotation  with 
the  wave-length  of  the  light  has  been  considered  theoretically  by 
several  writers,  and  the  theoretical  relations  have  been  applied  to 
the  experimental  data  available.  Such  data  appear,  however,  to 
be  rather  meager,  and  it  seemed  desirable  to  pursue  the  subject 
afresh  both  theoretically  and  experimentally. 

45 


461994 


46  R.  A.  CASTLEMAN,  JR.,  AND  E.  0.  HULBURT 

We  do  not  presume  to  attempt  a  historical  summary  of  the 
researches  on  the  many  aspects  of  this  subject.  For  a  summary  of 
the  earlier  work  we  make  reference  to  an  article  by  P.  Joubin.1 
Among  the  more  important  theoretical  formulae  for  the  magnetic- 
rotation  angle  in  terms  of  the  wave-length,  magnetic  field,  etc., 
were  those  obtained  by  Joubin,  Voigt,2  and  Drude.3  For  a  sum- 
mary of  the  experimental  measurements  of  the  magnetic-rotation 
angles  we -turn  to  the  Landoldt-Bornstein  Physical  Tables.  There 
the  data  have  been  tabulated  in  many  cases  as  the  Verdet  Constant, 
which  is  defined  to  be  the  angle  of  rotation  of  plane-polarized 
light  of  specified  wave-length  produced  by  a  medium  i  cm  in 
length  when  magnetized  by  a  longitudinal  magnetic  field  of  strength 
i  gauss.  These  measurements  were  applied  by  Joubin  and  Drude 
to  a  dispersion  theory  of  isotropic  media,  although  for  such  a  pur- 
pose the  experimental  data  were  hardly  sufficiently  numerous.  With 
the  exception  of  a  few  transparent  liquids  and  solids  the  Verdet 
Constant  was  found  either  for  unresolved  light  or  for  a  single  wave- 
length of  monochromatic  light.  In  the  cases  of  those  substances 
whose  Verdet  constant  has  been  determined  for  a  number  of  wave- 
lengths throughout  the  spectrum,  one  could  introduce  the  values 
into  a  suitable  dispersion  formula  to  test  a  dispersion  theory. 
Unfortunately,  however,  the  refractive  indices  of  most  of  these 
substances  do  not  conform  to  any  of  the  simpler  dispersion  for- 
mulae whose  constants  have  a  physical  interpretation,  and  so  these 
data  are,  from  this  standpoint,  uninteresting. 

In  the  present  work  transparent  liquids  were  chosen  whose 
dispersion  conformed  approximately  to  the  electronic  dispersion 
theory  of  H.  A.  Lorentz.4  The  angles  of  magnetic  rotation  of 
plane-polarized  light  for  a  series  of  wave-lengths  of  light  in  the 
visible  spectrum  were  measured.  A  formula  of  Lorentz  giving 
.the  relation  between  the  refractive  index  and  the  strength  of  the 
magnetic  field  was  modified  to  express  the  magnetic-rotation  angle 
in  terms  of  the  wave-length,  the  field  strength,  and  other  quantities. 
The  formula  was  found  to  agree  approximately  with  experiment  in 

1  Theses,  Faculte  des  Sciences,  Paris,  1888. 

*  Magneto-  und  Elektrooptik,  1908. 

3  Lehrbuch  der  Optik ,  1906.  *  Theory  of  Electrons,  1909. 


MAGNETIC  DISPERSION  IN  TRANSPARENT  LIQUIDS       47 

those  regions  of  the  spectrum  wherein  the  assumptions  upon  which 
it  was  based  were  valid. 

2.  Theoretical.  —  Suppose  plane-polarized  light  of  wave-length 
X  in  vacua  traverses  a  length  /  of  a  medium  of  refractive  index  ju 
for  the  wave-length  in  question  with  a  velocity  v.  If  the  medium 
is  placed  in  a  magnetic  field  of  strength  Hy  such  that  the  lines  of 
magnetic  force  are  parallel  to  the  direction  of  propagation  of  the 
light,  the  medium  becomes  doubly  refracting.  The  two  circularly 
polarized  components,  which  compose  the  plane-polarized  beam, 
now  pass  through  the  medium  with  velocities  vs  and  v2,  and  the 
medium  has  the  corresponding  refractive  indices  ^  and  yL2, 
respectively. 

Eddy,  Morley,  and  Miller,1  followed  by  Mills,2  have  shown  by 
an  interferometer  method  that 


or 


Mi     Ma     M 

This  was  determined  by  measurements  on  carbon  disulphide.  The 
accuracy  of  the  work  was  none  too  great,  because  the  experiment 
was  a  difficult  one;  but,  within  the  error  of  observation,  the  fore- 
going relation  was  true.  It  may  be  noticed  that  from  general  con- 
siderations one  would  not  expect  (i)  to  be  exactly  true,  and  further 
that  one  would  expect  the  difference  between  (i)  and  the  exact 
truth  to  be  small.  However,  we  now  assume  that  (i)  is  true  for 
all  the  substances  and  throughout  the  wave-length  range  used  in 
this  investigation. 

Let  6  be  the  observed  angle  in  radians  of  the  rotation  of  the 
plane  of  polarization  produced  by  the  magnetized  medium.  It  is 
easily  shown3  that 

\8  .  . 

M2-Mi  =  ^,  (3) 

where  X  is  the  wave-length  of  the  light  in  vacuo. 

1  Physical  Review,  7,  283,  1898. 

3  Ibid.,  i8;  65,  1904.  3  Drude,  loc.  cit.,  p.  396. 


48  R.  A.  CASTLEMAN,  JR.,  AND  E.  O.  HULBURT 

\f) 
Solving  (2)  and  (3)  for  ^  and  ^2,  and  considering  —  small 

compared  with  /*,  we  obtain 


, 

27T/ 


Let  us  turn  to  a  consideration  of  the  dispersion  theory  in  this 
connection.  We  restrict  the  discussion  to  isotropic,  transparent 
media  in  which  the  temperature  remains  constant.  We  use  the 
electron  theory  of  dispersion  as  given  by  H.  A.  Lorentz  (loc.  cit.). 
Let  £  and  Ex  be  the  X  components  of  the  displacement  of  the 
electron  from  its  equilibrium  position  and  the  electric  force, 
respectively,  77,  f ,  Ey  and  E2  are  the  7  and  Z  components  of  these 
quantities;  they  are  all  expressed  in  c.g.s.  electromagnetic  units. 
The  components  of  the  " restoring  force"  with  which  the  medium 
acts  upon  the  electron  are  /£,  /ry,  and  /f .  The  charge  on  the 
electron  in  c.g.s.  electromagnetic  units  is  e,  its  mass  is  m.  N  is  the 
number  of  such  electrons  per  unit  volume,  a-  is  a  constant  which 
Lorentz  has  shown  to  be  approximately  one-third  for  isotropic 
media.  The  external  magnetic  field  is  denoted  by  H  in  c.g.s. 
electromagnetic  units.  We  shall  suppose  H  to  have  the  direction 
of  the  axis  of  Z,  which  is  also  the  direction  of  the  propagation  of 
the  light.  The  magnetic  permeability  of  the  medium  is  taken  as 
unity. 

We  find  for  the  equations  of  motion  of  the  dispersion  electron 
of  a  single  type 


(5) 


-ft. 


Let  e  be  the  base  of  natural  logarithms,   and  let  all  dependent 

.2  ire  f. 

variables  of  (5)  contain  the  time  only  in  the  factor  e'~*~  where  - 

A 


MAGNETIC  DISPERSION  IN  TRANSPARENT  LIQUIDS        49 

is  the  frequency,  X  the  wave-length  of  the  vibration  in  vacuo,  and 
c  the  velocity  of  light  in  vacuo.  The  solution  of  (5)  gives  the 
refractive  index  fj.  as  determined  by  the  relation 


H, 


(6) 


where 


The  subscript  s1  is  used  to  denote  the  5th  type  of  electron.     —  is 

X5 

the  frequency  of  the  natural  undamped  vibration  of  this  electron. 
When  the  plus  sign  in  equation  (6)  is  used,  n  is  the  ju2  of  (4),  and 
when  the  minus  sign  is  used  ju  is  the  ^  of  (4). 

Equation  (6)  describes  fj,  in  terms  of  the  constants  of  a  single 
type  of  dispersion  electron.  There  may  be  other  types  of  disper- 
sion electrons  in  the  medium  with  constants  peculiar  to  the  type, 
so  that  in  the  more  general  case  the  right-hand  member  of  (6) 
becomes  a  summation  of  similar  terms,  one  term  for  each  type. 
For  this  case  the  complete  dispersion  formula  is 


(7) 


We  assume  we  are  dealing  with  a  region  of  the  spectrum  in 
whicji  the  change  of  the  refractive  index  with  wave-length  is 
determined  by  the  electrons  of  a  single  type,  so  that  in  the  sum- 
mation of  (7)  all  the  terms  except  one  may  be  replaced  by  a  quantity 
ql  which  is  independent  of  X  and  H.  Then  (7)  becomes 


.  (8) 

Li  , 


50  R.  A.  CASTLEMAN,  JR.,  AND  E.  0.  HULBURT 

where 


(9) 


2-Kcm 


A  special  case  occurs  when  H  is  zero.     For  this  (8)  becomes 
equivalent  to  the  well-known  dispersion  formula  of  Lorentz  : 


do) 


I     I 


Introducing  (4)  into  (8)  gives: 

L: =?i+T —    *  u    -  (i: 


It  was  expedient  to  transform  this  relation  to  one  more   amen- 
able to  arithmetical  computation.    This  was  readily  done  because 

\Q  TT 

-  and  —ht  were  smaller  than  the  other  quantities  appearing 

27T/  A 

with  them  in  the  denominators  by  a  different  order  of  magnitude. 
Equation  (n)  becomes  to  a  close  approximation 


6  is  in  radians. 

We  notice  that  if  we  use  either  the  two  plus  signs  of  (11)  or 
the  two  minus  signs,  we  arrive  at  the  same  equation  for  (12). 
This  shows  that  equation  (8)  is  in  close  agreement  with  (4)  .  We 
notice  also  that,  other  quantities  remaining  constant,  6  is  propor- 
tional to  /  and  H  in  turn.  This  agrees  with  the  experimental 
measurements  of  Rodger  and  Watson1  and  Dubois.2 

1  Phil.  Trans.  Roy.  Soc.,  A  186,  621,  1896.     This  paper  contains  further  references. 

2  Wied.  Ann.,  35,  137,  1888. 


MAGNETIC  DISPERSION  IN  TRANSPARENT  LIQUIDS       51 
If  <T  is  given  the  value  f ,  equation  (12)  becomes 


When  a  is  placed  equal  to  o,  equation  (12)  becomes 


irCAHl     MX*  ,* 

'  (I4) 


Formula  (14)  agrees  with  one  given  by  Voigt1  when  his  quantities 
are  expressed  in  c.g.s.  electromagnetic  units. 

To  compare  the  experimental  measurements  with  the  theory 
the  following  procedure  was  used.  Values  of  the  refractive  index 
of  the  liquid  under  investigation  for  wave-lengths  in  the  visible 
spectrum  were  taken  from  data  published  by  others.  Three 
values  of  M  and  the  corresponding  three  values  of  X  were  sub- 
stituted in  equation  (10),  and  the  three  constants  qlj  Cly  and  Xx 
were  computed.  Using  these  three  constants,  a  fourth  value  of  X 
was  substituted  in  (10)  and  the  value  of  M  calculated.  If  this 
value  of  n  agreed  approximately  with  the  observed  value,  the  sub- 
stance was  considered  to  conform  to  the  Lorentz  dispersion  equation 
(10)  for  the  region  of  the  spectrum  in  question.  The  values  of  6 
for  a  number  of  wave-lengths  in  the  visible  spectrum  were  meas- 
ured for  a  known  length  /  of  the  liquid  subjected  to  a  known 
magnetic  field  H.  The  constant  hi  was  then  determined  by 
substituting  in  equation  (13)  the  values  of  H,  I,  Cx,  X,,  and  the 
values  of  X,  6,  and  M  for  a  specified  wave-length.  6  was  then 
computed  by  means  of  (13)  for  the  other  wave-lengths,  and  the  com- 
puted value  was  compared  with  the  observed  value. 

3.  Experimental  arrangements.  —  The  arrangement  of  the  appa- 
ratus is  shown  in  plan  in  Figure  i.  A  gas-filled  lamp  with  a  spiral 
tungsten  filament  and  a  mercury-  vapor  lamp  served  as  sources  of 
light.  The  mercury-  vapor  lamp  was  used  for  observations  at 
wave-lengths  435.9  MM  and  546.  i  MM;  the  tungsten  lamp  was  used 
for  observations  from  the  green  to  the  red  end  of  the  spectrum. 

1  Loc.  cit.,  p.  130. 


R.  A.  CASTLEMAN,  JR.,  AND  E.  0.  HULBURT 


The  source  of  light,  shown  by  A,  Figure  i,  was  focused  on  the 
slit  Sj  of  the  spectrograph  by  a  lens  /x,  3  cm  in  diameter  and  of 
focal  length  22  cm. 

The  spectrograph  consisted  of  the  Littrow  mounting  of  a  plane 
grating.  The  grating  had  a  ruled  area  6  cm  by  7 . 5  cm  and  was 
ruled  15,000  lines  to  the  inch.  The  cone  of  light  from  slit  s^  was 
reflected  by  a  right-angle  glass  prism  through  the  large  lens  /2, 
10  cm  in  diameter  and  with  a  focal  length  of  75  cm.  The  spectrum 
was  brought  to  a  focus  at  slit  s2.  The  grating  was  mounted  on  a 
turntable  which  could  be  rotated  from  the  outside  of  the  case 
containing  the  spectrograph.  so  that  various  wave-lengths  of  light 
could  be  made  to  pass  through  the  second  slit.  The  grating 
possessed  a  bright  first  order,  and  this  first-order  spectrum  was 


FIG.  i 

used  throughout  the  present  work.  The  dispersion  was  such  that 
with  slit  s2  o.25mm  wide  a  beam  of  light  containing  a  wave- 
length range  of  5  A,  or  0.5  /zju,  passed  through.  Both  slit  sx  and 
slit  s2  were  always  o.  25  mm  in  width. 

The  monochromatic  beam  of  light  emerging  from  slit  s2,  after 
being  rendered  parallel  by  a  lens  /3,  2.5  cm  in  diameter  and  of 
focal  length  12.5  cm,  passed  through  the  polarizing  nicol  n^  and 
through  the  pierced  pole  pieces  of  a  Ruhmkorff  magnet  between 
which  the  cell  C  containing  the  liquid  under  investigation  was 
placed.  The  light  then  traversed  the  analyzing  nicol  prism  n2 
and  finally  entered  the  telescope  T.  .  The  lenses  /x,  /2,  and  lz  were 
achromatic  doublets. 

The  cell  which  contained  the  liquid  was  made  of  glass.  A 
short  length,  about  2  cm,  of  glass  tubing  of  internal  diameter  i  cm, 
to  which  had  been  sealed  a  small  side  tube,  was  ground  until  the 


MAGNETIC  DISPERSION  IN  TRANSPARENT  LIQUIDS       53 

ends  were  plane-parallel  to  within  0.003  cm-  Glass  plates  with 
optically  plane  surfaces  were  cemented  to  this.  Rubber  cement,  a 
mixture  of  lead  oxide  and  glycerine,  and  LePage's  liquid  glue,  were 
found  useful  as  cements  in  various  cases.  The  cell  was  filled 
through  the  side  tube.  The  length  of  the  column  of  liquid  was 
found  by  subtracting  the  thickness  of  the  end  plates  from  the 
external  length  of  the  cell.  The  liquids  used  were  obtained  from 
the  Chemical  Laboratory  and  were  of  a  high  degree  of  purity. 

The  pole  pieces  of  the  Ruhmkorff  magnet  were  elliptical  in 
shape  to  give  a  uniform  magnetic  field;  they  were  adjusted  to  be 
2 . 5  cm  apart.  To  calibrate  the  magnet,  the  angle  of  rotation  6 
for  sodium  light  was  observed  for  a  known  length  of  carbon  disul- 
phide  for  a  current  of  26.0  amperes  through  the  magnet.  From 
6  and  from  the  value  of  the  Verdet  constant  of  carbon  disulphide 
for  sodium  light,  which  has  been  carefully  determined  by  Rodger 
and  Watson  (loc.  cit.),  the  average  strength  of  the  magnetic  field 
between  the  pole  pieces  was  calculated,  and  was  found  to  be 
6480  gauss.  This  field  strength  was  used  for  all  the  rotation 
measurements  of  this  paper.  It  was  found  by  tests  that  the  rota- 
tion angle  6  had  the  same  absolute  value  for  the  magnetic  field 
direct  and  reversed.  This  indicated  that  hysteresis  effects  in  the 
magnet  were  negligible. 

The  mounting  of  the  analyzing  nicol  carried  a  circular  scale 
which  measured  the  rotation  angles  to  one-tenth  of  a  degree  of  arc. 
It  was  found  that  the  analyzer  could  be  set  for  extinction  for  all 
the  wave-lengths  with  a  precision  of  two-tenths  of  a  degree.  The 
values  of  the  rotation  angle  were  in  all  cases  the  means  of  at  least 
four  measurements,  two  taken  with  the  field  direct  and  two  with 
the  field  reversed.  It  was  considered  that  the  mean  angle  was 
correct  to  one-tenth  of  a  degree  of  arc. 

4.  Errors  and  corrections. — No  correction  was  made  for  the 
error  due  to  scattered  light.  There  were  two  ways  in  which 
scattered  light  might  introduce  systematic  error  into  the  rotation 
measurement,  the  first  arising  from  light  scattered  by  the  grating, 
and  the  second  from  multiple  reflections  by  the  surfaces  at  the 
ends  of  the  cell  which  held  the  liquid.  To  determine  the  effect  of 
the  light  scattered  by  the  grating,  the  beam  issuing  from  slit  s2  was 
examined  with  a  transmission  grating.  When  the  tungsten  lamp 


54  R-  A.  CASTLEMAN,  JR.,  AND  E.  O.  HULBURT 

was  used  as  the  source  of  light,  it  was  found  that  the  beam  con- 
tained light  of  foreign  wave-lengths  of  rather  feeble  intensity;  in 
the  case  of  the  mercury  lamp  this  foreign  light  appeared  still 
weaker.  Upon  looking  into  the  telescope  and  setting  the  analyzer 
for  extinction  it  was  found  that  the  image  of  slit  Si  did  not  fade 
out  against  an  absolutely  black  background.  Very  faint  light  was 
seen  in  the  field,  due  no  doubt  to  the  light  scattered  by  the  grat- 
ing and  to  imperfections  throughout  the  optical  system.  The 
settings  for  extinction  could,  however,  be  made  with  precision, 
and  it  was  deemed  that  the  extraneous  light  introduced  no  appreci- 
able systematic  errors.  Any  error  due  to  multiple  reflections  from 
the  surfaces  of  the  ends  of  the  glass  cell  was  avoided  by  rotating 
the  cell  slightly  until  these  surfaces  were  not  perpendicular  to  the 
beam  of  light.  The  error  which  this  caused  in  the  determination 
of  /  was  negligible. 

TABLE  I 

x  e 

436  HfJL  1.7° 

503  i-3 

546  0.9 

579  0-85 

589  0.85 

620  0.8 

It  had  been  feared  that  errors  due  to  temperature  would  be 
troublesome,  but  it  was  found  that  these  fears  were  needless.  To 
carry  out  a  complete  series  of  measurements  of  the  rotation  angle 
for  five  wave-lengths  in  the  visible  spectrum  required  about  an 
hour.  During  this  time  the  magnet  heated  up,  and  the  tempera- 
ture of  the  liquid  in  the  cell  increased.  The  increase  was  never 
more  than  3°  C.  In  the  case  of  carbon  disulphide  the  temperature 
coefficient  of  the  Verdet  constant  for  sodium  light  has  been  deter- 
mined.1 A  three-degree  change  in  temperature  changed  the  Verdet 
constant  by  about  0.5  per  cent.  In  the  present  case  it  was 
considered  that  errors  due  to  temperature  changes  were  for  the 
most  part  less  than  0.5  per  cent,  and  that  it  was  unnecessary  to 
arrange  a  more  accurate  control  of  the  temperature  of  the  liquid 
in  the  cell. 

1  Rodger  and  Watson,  loc.  cit. 


MAGNETIC  DISPERSION  IN  TRANSPARENT  LIQUIDS       55 

The  rotation  angle  6  due  to  the  liquid  alone  was  obtained  from 
the  observed  rotation  angle  produced  by  the  liquid  in  the  cell  by 
subtracting  from  this  observed  angle  the  angle  of  rotation  pro- 
duced by  the  empty  cell  for  the  wave-length  in  question.  Table  I 
shows  0  for  the  two  glass  plates-  on  the  ends  of  the  cell.  The 
thickness  of  the  two  plates  together  was  o.  315  cm,  the  field  strength 
was  6480  gauss.  The  magnetic-rotation  angles  plotted  in  the 
figure  have  in  all  cases  been  corrected  for  the  effect  of  the  glass 
ends  of  the  cell. 

5.  Carbon  disulphide. — The  data  for  this  substance  and  the 
results  of  the  calculations  are  given  in  Table  II  and  Figure  2.  We 
shall  discuss  these  in  some  detail,  and  shall  avoid  a  repetition  of 
the  discussion  for  the  other  substances.  The  observed  values  of 
6,  shown  by  circles  in  Figure  2,  have  been  plotted  as  ordinates 
against  wave-lengths  as  abscissae;  a  smooth  line,  curve  i,  has 
been  drawn  through  them.  The  strength  of  the  magnetic  field, 
the  length  of  the  layer  of  liquid,  and  the  temperature  at  the  begin- 
ning and  the  end  of  the  experiment  are  shown  in  the  first  two  lines 
of  Table  II. 

Verdet1  has  recorded  relative  values  of  6  for  carbon  disulphide 
for  a  number  of  wave-lengths  in  the  visible  spectrum.  The  mag- 
netic field  used  was  not  mentioned.  For  the  sake  of  comparison 
the  values  given  by  Verdet  have  been  reduced  to  agree  with 
curve  i  for  \  $89 . 3  pp  and  are  shown  by  crosses  in  Figure  2. 
Joubin  (loc.  cit.}  also  carried  out  measurements  on  carbon  disul- 
phide. Neither  the  magnetic  field,  nor  the  length  of  the  liquid, 
nor  the  temperature  were  recorded.  By  a  coincidence  his  value 
for  6  at  X  589.3  MI  was  the  same  as  that  of  curve  i,  namely  io?3. 
His  values  have  been  plotted  as  dots  in  Figure  2.  We  think  that 
the  measurements  of  curve  i  were  correct,  for  they  were  repeated 
with  precision  a  few  weeks  later. 

In  order  to  introduce  these  experimental  results  into  the  dis- 
persion formula  (10)  we  assume  that  the  absorption  of  carbon 
disulphide  is  inappreciable  for  the  visible  wave-lengths  in  question. 
Such  an  assumption  is  manifestly  not  accurate,  because  this  sub- 
stance absorbs  the  blue  end  of  the  spectrum  to  a  certain  extent. 

1  Verdet,  Oeuvres  completes. 


R.  A.  CASTLEMAN,  JR.,  AND  E.  O.  HULBURT 


We  take  the  values  of  the  refractive  index  found  at  2o?o  C.  by 
Flatow.     These  and  the  corresponding  wave-lengths  are  shown  in 

the  third  and  fourth  lines  of  Table  II. 
Substituting  these  values  into  for- 
mula (10),  the  values  of  the  constants 
Ci,  qly  A!  were  computed  and  are 
tabulated  in  the  fifth  line  of  Table  II. 
The  agreement  between  (10)  and  ob- 
servations was  tested  by  using  the 
foregoing  values  of  the  constants  and 
computing  ju  for  X  394  juju  to  be  i .  7043. 
The  observed  value  was  i .  70226,  and 


20° 


10° 


Carbon  disulphide 


MZO 


500/xyui 

FIG.  2 

TABLE  II 

CARBON  BISULPHIDE 


600 


#=648ogauss  7=2.272  cm 

/      Temp.  2i?2  to  22?oC. 

\44i.6ji/i  508.6  589.3 

fj,  i. 67180  1.64586          1.62806  at  20?o  C. 

Observed  by  Flatow,  Ann:  d.  Phys.<  12,  85,  1903. 


d=io.38iXio8 


57272 


Xi=204. 


X  394  nn 


observed  ju=  i  .70226 
calculated  JJL  =  i .  7043 


-s  forX  589. 3 


MAGNETIC  DISPERSION  IN  TRANSPARENT  LIQUIDS        57 

the  agreement  was  considered  sufficiently  close.  These  numbers 
are  given  in  lines  7  and  8  of  Table  II.  The  dispersion  of  carbon 
disulphide  and  a-monobromnapthalene  has  been  more  fully  dis- 
cussed in  a  former  paper.1 

The  constant  hi  was  then  determined  by  substituting  in  equation 
(12)  the  values  of  H,  /,  Ct,  and  Xj  given  in  Table  II,  and  the  values 
of  X,  6,  and  ^  for  the  wave-length  589  .  3  /z/i.  This  gave  3  .  95  X  io~5 
for  hi,  as  shown  in  the  last  line  of  Table  II,  when  all  the  quantities 
were  expressed  in  c.g.s.  and  c.g.s.  electromagnetic  units. 

The  constants  of  (13)  were  now  completely  known,  and  (13) 
was  then  used  to  compute  the  values  of  0  for  the  range  of  the 
spectrum  under  investigation.  The  computed  curve  is  shown  by 
the  dotted  line,  curve  2,  of  Figure  2.  It  is  seen  that  the  agreement 
between  the  observed  and  calculated  values  of  6  was  fairly  close 
for  the  longer  wave-lengths,  but  that  for  the  shorter  wave-lengths 
the  theoretical  value  was  greater  than  the  observed  value,  the 
difference  between  the  two  values  increasing  as  the  wave-length 
decreases.  This  difference  between  theory  and  experiment  may 
be  attributed,  in  part  at  least,  to  the  neglect  of  the  effect  of  absorp- 
tion in  the  theory.  The  discrepancy  was  in  the  right  direction  to 
be  attributed  to  this  effect,  for  the  introduction  into  the  theoretical 
formula  of  terms  denoting  absorption  will  produce  a  decrease  in  the 
computed  values  of  6  for  the  shorter  wave-lengths. 

In  his  treatise  on  optics  Drude2  has  derived  two  theoretical 
expressions  for  the  magnetic  rotatory  dispersion  of  isotropic  media, 
one  based  on  the  "molecular  stream"  hypothesis,  and  the  other  on 
the  "Hall  effect"  hypothesis.  When  written  in  a  form  to  show  the 
connection  between  6  and  X,  neglecting  absorption,  the  two  formulae 
were,  respectively, 


and 


1  A  str  -o  ^physical  Journal,  46,  i,  1917. 

2  Loc.  cit.,  p.  406. 


58  R.  A.  CASTLEMAN,  JR.,  AND  E.  0.  HULBURT 

aly  a2,  a3,  and  a4  were  quantities  which  involved  the  masses,  the 
charges,  and  the  numbers  of  the  "bound"  and  "free"  electrons, 
the  strength  of  the  magnetic  field,  the  length  of  the  medium,  etc. 
The  refractive  index  wave-length  relation  in  this  connection  was 


(17) 


Drude  applied  these  equations  to  Verdet's  magnetic-rotation  meas- 
urements on  carbon  disulphide  and  creosote  in  the  following  man- 
ner. Using  the  value  of  Xx  obtained  from  (17)  and  two  known 
values  each  of  6  and  X,  the  remaining  two  constants  of  (15)  or  (16) 
were  determined.  The  0-X  curve  from  either  formula,  which  thus 
traversed  two  of  the  observed  points,  was  found  to  pass  closely  to 
the  remaining  observed  points.  We  do  not  believe,  however,  that 
the  agreement  found  in  this  way  between  theory  and  experiment 
possesses  great  significance.  One  would  not  expect  a  theory  which 
neglected  absorption  to  portray  the  observations  with  great 
exactness. 

Joubin  (loc.  cit.)  has  also  derived  a  formula  for  the  dispersion 
of  magnetic  rotation  of  somewhat  the  same  type  as  (15).  He 
applied  this  to  the  observations  of  rotations  of  carbon  disulphide 
and  creosote,  which  were  measured  for  the  purpose,  in  much  the 
same  manner  as  done  by  Drude. 

6.  a-monobromnaphthalene.  —  This  substance  was  investigated 
in  a  manner  similar  to  that  described  in  the  case  of  carbon  disul- 
phide.   Table  III  shows  a  portion  of  the  data  and  the  results  of 
the  calculations.     This  table  has  been  compiled  exactly  as  was 
Table  II  for  carbon  disulphide,  and  therefore  requires  no  further 
explanation.     The  observed  values  of   6  have  been  plotted   as 
circles  in  Figure  3,  and  a  smooth  line,  curve  i,  has  been  drawn 
through  them.     The  computed  values  of  6  from  equation  (13), 
using  the  constants  of  Table  III,  are  shown  by  the  dotted  line, 
curve  2,  of  Figure  3.     The  differences  between  the  observed  and 
theoretical  values  are  similar  to  those  noted  for  carbon  disulphide. 

7.  Benzene.  —  The  values  of  6  for  this  substance  were  deter- 
mined  throughout  the  visible  spectrum.     These  are  shown  by 
circles  in  Figure  4,  through  which  a  smooth  line,  curve  i,  has  been 


MAGNETIC  DISPERSION  IN  TRANSPARENT  LIQUIDS       59 

passed.     The  Verdet  constant  of  benzene  was  found  by  Jahn1  to 

be  0.0297  minutes  of  arc  for  sodium 

30°[_  light.     From  the  data  of  Figure  4  and 

Table  IV  we  obtain  0.0291  minutes 
of  arc  for  the  same  wave-length. 
Jahn's  value  is  not  far  different  from 
this. 

The  computed  values  of  6  from 
equation  (13)  are  shown  by  the  dotted 
line,  curve  2,  of  Figure  4.     It  is  seen 
that  the  differences  between 
the  observed  and  theoreti- 

20°L  \\  cal  values  are  of  the  same 

character   as   those   of   the 
previous  cases. 


I2C 


CX-TTI  on  obrom  naphthalene 


H20 


SOOjuym 

FIG.  3 


600 


TABLE  III 

tt-MONOBROMNAPHTHALENE 


=  6480  gauss 


Temp. 


to  2o?y  C. 


£=2.272  cm 


X  434  MM  486  589 

M  i.  70433  1.68245          1.65876  at  i9?4  C. 

Observed  by  Briihl,  Ber.  Chem.  Ges.,  22,  388,  1897. 


. 398X108 


^=0.70889 


X  656  ju/j 


observed  /x=  i  .64995 
calculated  /x=  i  .6500 


7^=5.02X10-5  forX  589.3 


1  Wied.  Ann.,  43,  280,  1891. 


6o 


R.  A.  CASTLEMAN,  JR.,  AND  E.  O.  HULBURT 


8.  Nitrobenzene. — The  results  of  the  work  on  this  substance  are 
shown  in  Table  V  and  Figure  5.     The  observed  values  of  6  were 

plotted  as  circles  in  Figure  5,  and  a 

•  col      \  smooth  line,  curve  i,  has  been  drawn 

\  through  them.    The  computed  values 

\  of  6  from  equation   (13)  are  shown 

by  the  dotted  line,  curve  2. 

Discrepancies  of  the  same  char- 
acter exist  between  the  observed  and 
theoretical  values  of  6  as  were  noticed 
in  the  preceding  cases,  but  perhaps 
greater  in  magnitude. 


10' 


6° 


Banzene 


M20 


600 


FIG.  4 

TABLE  IV 
BENZENE 


77=6480  gauss 


Temp.  22?9  to  24^6  C. 


/=2.28o  cm 


X  434  nfj,  486  589 

ju  i*. 52380  1.51323  1.50111 

Landoldt-Bornstein  Tables. 


at  2o?o  C. 


0.49898 


«  173.8  AM« 


X  656  fJLfJL 


observed  ju=  i  .49646 
calculated  ju=  i  .4964 


-5  for  X  589.3  /z/z 


\ 


MAGNETIC  DISPERSION  IN  TRANSPARENT  LIQUIDS       61 

9.  Ethyl  iodide. — The  circles  of  Figure  6  show  the  observations 
on  this  substance;  a  smooth  line,  curve  i,  has  been  drawn  through 

the  observed  points.  Other  data  are 
given  in  Table  VI.  Perkin1  had  de- 
termined the  Verdet  constant  of 
ethyl  iodide  to  be  0.0296  minutes  of 
arc  for  sodium  light.  From  the  pres- 
ent data  we  find  0.0300  for  this  wave- 
length. The  two  values  are  not 
\  greatly  at  variance.  The  computed 

x  2         values  of  6  from  equation  (12)   are 
V      shown  by  the   dotted  line,  curve  2, 


1 


10° 


Nitrobenzene 


H20 


500/x/x 

FIG.  5 

TABLE  V 

NITROBENZENE 


600 


H  =  6480  gauss  /=  2. 272  cm 

Temp.  2i?4  to  22^6  C. 


\4S6.2fjLfji          589.3  656.3 

AIL  57165  I.553I9  1-54641 

Landoldt  Bornstein  Tables. 


at  2o?o  C. 


6.o66Xio8' 


=o. 62924 


X  434 . i 


observed  jj,=  i .  5895 
calculated  M  =1.5888 


/Z!=2.56Xio~5  for  X  589.3 


Smithsonian  Physical  Tables,  1920. 


62 


R.  A.  CASTLEMAN,  JR.,  AND  E.  O.  HULBURT 


Figure  6.     It  is  seen  that  the  discrepancies  between  the  observed 

and  theoretical  values  are  similar  to 
those  of  the  preceding  cases. 

10.  Discussion  of  results. — It  has 
been  demonstrated  that  the  formula 
(13),  which  has  been  developed  from 
the  electron  theory  of  Lorentz,  served 
to  express  with  a  certain  exactitude 
the  dispersion  of  the  magnetic  rota- 
tion of  certain  liquids  throughout 
the  visible  spectrum.  For  the  longer 


10° 


Ethyl  iodide 


420 


500/jiM 


600 


FIG.  6 

TABLE  VI 
ETHYL  IODIDE 


gauss 


Temp. 


to 


C. 


/=2.220  CHI 


X486.2JU/I          589.3  656.3 

n  i. 52356    1.51203    1.50738 

Observed  by  Lorentz,  Wied.  Ann.,  n,  70,  1880. 


at  2o?o  C. 


<7i=o.  50762 


X  434 . i 


observed  /*  =  i .  5343  7  * 
calculated  JJL=  i . 5336 


7^=5. 90X10-5  for  X  589.3^ 


*Haagen,  Pogg.  Ann.,  131,  117,  1866. 


MAGNETIC  DISPERSION  IN  TRANSPARENT  LIQUIDS       63 

wave-lengths  of  the  visible  spectrum  the  agreement  between  theory 
and  experiment  is  quite  close.  For  the  shorter  wave-lengths  dis- 
crepancies occur  which  increase  as  the  wave-length  decreases. 
The  liquids  investigated  above  possess  strong  absorption  in  the 
ultra-violet  and  appreciable  absorption  in  the  blue  end  of  the 
spectrum.  We  may  therefore  reasonably  attribute  the  discrepancy 
between  theory  and  experiment  in  large  part  to  the  neglect  of 
absorption.  If  absorption  is  taken  into  account  in  our  equations, 
Xi  is  increased,  and  in  general  the  modification  which  the  constants 
of  the  equations  undergo  is  such  as  to  bring  the  theoretical  values 
of  0  into  closer  agreement  with  the  observed  ones.  The  absorp- 
tion of  these  substances  for  light  has,  however,  not  been  meas- 
ured accurately,  and  it  seems  unprofitable  at  this  time  to  consider 
its  effect  numerically, 

ii.  The  values  of  e/m.  —  From  the  known  value  of  hl}  the  ratio 
of  the  charge  to  the  mass  of  the  electron  may  be  calculated  by 

TABLE  VII 

A,  e/m 

Carbon  disulphide  ............  3.95X10"$  0.74X10? 

a—  monobromnaphthalene.  .  .  .  -5.02  0.95 

Benzene  ....................   5  .34  i  .01 

Nitrobenzene  ................   2.56  0.49 

Ethyl  iodide  .................   5  .  90  1.12 

means  of  formula  (9).  This  has  been  done  and  the  results  are 
shown  in  Table  VII;  e/m  is  expressed  in  c.g.s.  electromagnetic 
units. 

Becquerel1,  Voigt,2  and  Siertsema3  have  derived  formulae  for 
the  dispersion  of  the  magnetic  rotation,  by  means  of  which  e/m 
can  be  found  as  soon  as  the  Verdet  constant  and  the  dispersion 
dfji/dK  of  a  substance  for  the  same  wave-length  X  are  known.  These 
three  formulae  reduce  to  the  same  one,  namely 


m 


X  IE  '  d\  ' 


1  Comptes  rendus,  125,  679,  1899. 

a  Wied.  Ann.,  67,  351,  1899.  3  Comm.  Lab.  Leiden,  No.  82,  1902. 


64  R.  A.  CASTLEMAN,  JR.,  AN£>  E.  O.  HULBURT 

Using  (18),  Siertsema  computed  e/m  for  air,  carbon  dioxide,  hydro- 
gen, water,  carbon  disulphide,  and  quartz.  The  numbers  varied 
from  o .  75  X  io7  to  i .  77  X  io7. 

12.  The  effect  of  a  upon  the  calculations. — The  value  of  the 
quantity  cr  has  no  very  critical  effect  upon  the  variation  of  6  with 
wave-length.  The  calculated  curves  of  the  diagrams  have  been 
obtained  by  the  use  of  J  for  cr  in  formula  (12).  If  a  is  put  equal 
to  o  in  (12),  we  arrive  at  Voigt's  formula  (14),  and  if  this  is  used 
to  calculate  the  change  of  6  with  X  we  find  values  of  6  which  are  a 
trifle  less  than  those  obtained  from  (13).  They  are  about  i  per 
cent  less  at  X  434  juju,  but  are  practically  the  same  for  wave-lengths 
greater  than  500  /zju.  If  cr  is  given  values  greater  than  f ,  the  com- 
puted values  of  0  are  found  to  be  somewhat  greater  than  the 
values  given  by  (13),  and  therefore  in  greater  discordance  with  the 
observed  values.  For  example,  in  the  case  of  carbon  disulphide, 
if  c7  =  f,  0is  25?!  at434ju/z. 

The  values  of  e/m  change  to  some  extent  when  cr  is  given 
different  values.  This  is  shown  for  carbon  disulphide  in  Table 
VIII.  We  conclude  that,  as  far  as  the  present  data  are  concerned, 

TABLE  VIII 

<r  e/m 

0  1.78X107 

1  0-74 

I  0.30 

I  0.25 

it  makes  little  difference  whether  cr  is  o  or  J.  If,  however,  a  is 
increased  above  J,  the  discrepancies  between  the  theory  and  the 
observations  become  greater. 

In  conclusion  the  authors  take  pleasure  in  expressing  their 
thanks  to  Dr.  J.  S.  Ames  for  valuable  and  constructive  criticism. 

JOHNS  HOPKINS  UNIVERSITY 
February  1921 


VITA 

Robert  Allen  Castleman,  Jr.,  son  of  Robert  Allen  and  Fannie  (Funsten) 
Castleman,  was  bora  at  The  Hague,  Westmoreland  Co.,  Virginia,  on 
January  4,  1892.  He  graduated  at  the  Baltimore  City  College  in  1909, 
and  then  attended  undergraduate  courses  at  the  Johns  Hopkins  Univer- 
sity during  the  three  years,  1910-13.  He  taught  at  the  Episcopal  High 
School,  Alexandria,  Virginia,  from  1913-15,  and  took  his  A.B.  degree 
at  George  Washington  University  in  1915.  During  the  year  1915-16  he 
was  assistant  in  physics  at  Tulane  University,  taking  graduate  courses 
in  physics  and  mathematics.  He  returned  to  Johns  Hopkins  University 
in  1916  as  a  graduate  student  in  physics  and  electrical  engineering, 
taking  his  M.A.  degree  at  that  institution  in  1917.  From  1917-20  he 
was  at  the  Bureau  of  Standards,  holding  positions  of  laboratory  assistant 
and  assistant  physicist.  At  the  same  time  he  continued  his  studies 
under  the  direction  of  Professor  Ames.  He  returned  to  Johns  Hopkins 
in  1920,  taking  work  in  physics,  mathematics,  and  applied  mathematics. 
He  has  had  lectures  under  Professors  Ames,  Wood,  Pfund,  Bliss, 
Whitehead,  Cohen,  and  Murnaghan. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  FINE  OP  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


DEC  2.1  i«a§ 

**AR  1*  19, 

aut*1& 

•  jS&^ 

V3\vw 

,  1  t  r  •,--,  rrj  ft 

20^tP  52HU 
t  , 

SEP2Q^ 

ill/-  — 

REC'D  LD 

OCT27'63-4PM 

LD  21-95m-7,'37 

